Basic properties
| Modulus: | \(8015\) | |
| Conductor: | \(8015\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(228\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8015.hn
\(\chi_{8015}(88,\cdot)\) \(\chi_{8015}(93,\cdot)\) \(\chi_{8015}(263,\cdot)\) \(\chi_{8015}(352,\cdot)\) \(\chi_{8015}(578,\cdot)\) \(\chi_{8015}(788,\cdot)\) \(\chi_{8015}(793,\cdot)\) \(\chi_{8015}(802,\cdot)\) \(\chi_{8015}(1052,\cdot)\) \(\chi_{8015}(1353,\cdot)\) \(\chi_{8015}(1458,\cdot)\) \(\chi_{8015}(1488,\cdot)\) \(\chi_{8015}(1502,\cdot)\) \(\chi_{8015}(1712,\cdot)\) \(\chi_{8015}(2027,\cdot)\) \(\chi_{8015}(2053,\cdot)\) \(\chi_{8015}(2202,\cdot)\) \(\chi_{8015}(2277,\cdot)\) \(\chi_{8015}(2312,\cdot)\) \(\chi_{8015}(2342,\cdot)\) \(\chi_{8015}(2487,\cdot)\) \(\chi_{8015}(2517,\cdot)\) \(\chi_{8015}(2573,\cdot)\) \(\chi_{8015}(2662,\cdot)\) \(\chi_{8015}(2718,\cdot)\) \(\chi_{8015}(3007,\cdot)\) \(\chi_{8015}(3063,\cdot)\) \(\chi_{8015}(3152,\cdot)\) \(\chi_{8015}(3208,\cdot)\) \(\chi_{8015}(3238,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{228})$ |
| Fixed field: | Number field defined by a degree 228 polynomial (not computed) |
Values on generators
\((3207,4581,4586)\) → \((-i,e\left(\frac{2}{3}\right),e\left(\frac{75}{76}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) | \(16\) |
| \( \chi_{ 8015 }(88, a) \) | \(1\) | \(1\) | \(e\left(\frac{46}{57}\right)\) | \(e\left(\frac{41}{228}\right)\) | \(e\left(\frac{35}{57}\right)\) | \(e\left(\frac{75}{76}\right)\) | \(e\left(\frac{8}{19}\right)\) | \(e\left(\frac{41}{114}\right)\) | \(e\left(\frac{61}{114}\right)\) | \(e\left(\frac{181}{228}\right)\) | \(e\left(\frac{27}{38}\right)\) | \(e\left(\frac{13}{57}\right)\) |